Frank-Tamm formula

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The Frank-Tamm formula yields the amount of Cherenkov radiation emitted as a charge particle moves through a medium at superluminal velocity.

When a charged particle moves faster than the speed of light in a medium, it can emit a photon while conserving energy and momentum, this process can be viewed as a decay.

[edit] Equation

The Energy emitted per unit length (travelled by the particle) per unit frequency is:

$dE = \frac{\mu(\omega) q^2} {4 \pi} \omega (1 - \frac{c^2} {v^2 n(\omega)^2}) dx d\omega$ ,

where $μ$ and $n (ω)$ are the permeability and index of refraction of the medium, $q$ is the electric charge of the particle, $v$ is the speed of the particle, $c$ is the speed of light in vacuum, and $ω$ is the angular frequency of radiation.